1. Technical Field
The present invention relates to a resonator element, a resonator having the resonator element, and an oscillator having the resonator element.
2. Related Art
In the related art, a tuning-fork type piezoelectric resonator element (hereinafter referred to as a resonator element) in which a pair of resonating arms alternately vibrates in the flexural vibration mode in the direction towards or away from each other is widely used as a resonator element.
A loss of vibration energy when such a resonator element vibrates in the flexural vibration mode leads to an increase of the CI (Crystal Impedance) value or a decrease of the Q value and thus causes deterioration of performances. Here, the CI value is a value which serves as an indicator of the likelihood of oscillation, and the lower it is, the more the resonator element is likely to oscillate. The Q value is a dimensionless number representing a vibration state, and the higher it is, the more the resonator element vibrates stably.
Thermal conduction is considered as one of the causes of the loss of vibration energy.
FIG. 4A is a diagram illustrating thermal conduction in a resonator element. As shown in FIG. 4A, a resonator element 151 includes two parallel resonating arms 153 and 154 extending from a base portion 152.
When a predetermined voltage is applied to an electrode (not shown) in such a state, the resonating arms 153 and 154 vibrate in the direction towards or away from each other. When the resonating arms 153 and 154 are moved away from each other, compressive stress acts on hatched regions A (the outer root portions of the resonating arms 153 and 154), and tensile stress acts on hatched regions B (the inner root portions of the resonating arms 153 and 154).
When the resonating arms 153 and 154 are moved towards each other, tensile stress acts on the hatched regions A, and compressive stress acts on the hatched regions B.
At that time, temperature increases in the regions where compressive stress acts and decreases in the regions where tensile stress acts.
The resonator element 151 loses vibration energy due to heat transfer (thermal conduction) occurring due to equilibration of temperature between a contracted portion of the resonating arms 153 and 154 where compressive stress acts and an expanded portion where tensile stress acts.
A decrease of the Q value caused by such thermal conduction is referred to as thermoelastic loss.
From the relationship between distortion and stress which is well-known as a phenomenon of internal friction of a solid generally occurring due to a temperature difference, the thermoelastic loss is described as follows. In a flexural vibration-mode resonator element, when the vibration frequency changes, the Q value reaches the minimum at a relaxation vibration frequency fm (=½πτ; here, τ is a relaxation time).
The relationship between the Q value and the frequency is generally expressed as a curve F in FIG. 4B. In the drawing, the frequency at which the Q value reaches the minimum Q0 is a thermal relaxation frequency f0 (=½πτ).
Moreover, a region (1<f/f0) on the high frequency side in relation to a boundary of f/f0=1 is an adiabatic region, and a region (f/f0<1) on the low frequency side in relation to the boundary is an isothermal region.
FIGS. 5A and 5B are schematic diagrams showing a simplified configuration of a resonator element of the related art. FIG. 5A is a planar diagram, and FIG. 5B is a cross-sectional diagram taken along the line C-C in FIG. 5A.
As shown in FIGS. 5A and 5B, a resonator element 100 includes tuning-fork arms (hereinafter referred to as resonating arms) 102 and a tuning-fork base portion (hereinafter referred to as a base portion) 104. A groove 106 is formed on the upper and lower surfaces of each of the resonating arms 102, and electrodes 110 and 112 are disposed on the side surfaces of the groove 106.
The resonator element 100 also includes electrodes 114 and 116 which have different polarities and which are disposed on the side surfaces of each of the resonating arms 102 so as to face the electrodes 110 and 112 (for example, see JP-A-2005-39767).
In the resonator element 100 disclosed in JP-A-2005-39767, as shown in FIG. 5B, a thermal conduction path between the contracted portion and the expanded portion of the resonating arms 102 is narrowed in the midway by the grooves 106.
As a result, in the resonator element 100, a relaxation time τ up to the equilibration of the temperature of the contracted portion and the expanded portion increases.
Therefore, in the resonator element 100, since the grooves 106 are formed, in the adiabatic region shown in FIG. 4B, the shape of the curve F itself does not change, but with a decrease of the thermal relaxation frequency f0, the curve F shifts to the position of a curve F1 in the lower frequency direction. The curve F1 shows a state in which no electrode is formed in the groove 106.
As a result, in the resonator element 100, the Q value increases as indicated by the arrow a.
However, in the resonator element 100, when the electrodes 110 and 112 are formed in the grooves 106, the curve F shifts to the position of a curve F2, and the Q value decreases as indicated by the arrow b.
A thermal conduction path formed by the electrodes 110 and 112 can be considered as one of the reasons thereof.
That is, a conductive material such as an electrode material has higher thermal conductivity than a quartz crystal which is a piezoelectric material used as a base material of the resonator element 100. In such a conductive material, electrons as well as phonons of metal carry thermal energy.
Specifically, in the resonator element 100, as indicated by the arrows in FIG. 5B, since thermal conduction is carried out by the electrodes 110 and 112 as well as a quartz crystal, the relaxation time τ decreases, and with an increase of the thermal relaxation frequency f0, the curve F shifts to the position of the curve F2 in the higher frequency direction.
In order to solve this problem, a configuration in which the electrodes on the bottom portion of the groove are removed to suppress thermal conduction by the electrodes on the bottom portion, thus increasing the relaxation time τ may be considered.
However, with progress in the miniaturization of the resonator element, it is difficult to sufficiently improve the relaxation time τ just through removal of the electrodes on the bottom portion of the groove. Thus, it is not possible to achieve a sufficient improvement of the Q value.